This is a build for Kassadin to let him succeed early on. Playing Kassadin, I like to harass early on but with other builds that go Mana first, this cannot be accomplished as easily. This build is designed to be a lane pushing, harassing but then scaling to be more powerful mid/late game. I like this build because after Kassadin gets his ultimate, he can escape much easier by Riftwalking through walls, or just in front of him to get ahead of gankers/attackers. So since he can always have a good chance of escaping, he can be more aggressive, greedy and just overall more...Bloodthirsty!

Kassadin's Passive is Void Stone, which reduced magic damage by 15% and with each point of ignored damage, your attack speed is increased by 1%.

Kassadin's First Spell or Q is Null Sphere. This is your base spell, it is one of your most damaging spells and it has a silence which increases with it's level. This is to be maxed first.

Kassadin's Second Spell or W is Nether Blade. This passively allows for Kassadin's attacks to restore mana and when activated it charges your normal auto attacks to do bonus damage. I take one point in this and max it last.

Kassadin's Third Spell or E is Force Pulse. This spell is used when chasing or attacking a larger group of enemies because it damages and slows enemies in a cone. Although in early game, it may be difficult to get chargers, when it is released it does a fair ammount of damage.

Kassadin's Ultimate or R is Riftwalk. This spell has all sortes of uses but it is boiled down to a flash that you can use more often. If you used the spell again shortly after using it it will increase the damage and mana cost. This is good but it can drain your mana if you are not careful!

Since this build is designed to be aggressive early game, many of the late game items can be changed to fit personal preference. I get Rylai's Crystal Scepter first for the early Ability Power. But an example of some changes could be to change any of the last big four items for Mejai's Soulstealer if you feel your are doing well and it will pay off. The biggest variable in my opinion is Void Staff because it depends if the enemy team has alot of magic resist, and if they don't, it can be changed to Mejai's Soulstealer therefore getting Mejai's earlier in the game or it can be changed to Banshee's Veil therefore getting Catalyst the Protector early game to reduce return trips to the fountain. Some of the other items that could be changed in late game are:
Abyssal Scepter; if the enemy has more magic damage but if not it dosen't really pay off.
Rod of Ages; but since it's passive stacks every minute, it's better to get it earlier in the game not the last item.
Deathfire Grasp; to kill those enemy Champions with more HP.
Moonflair Spellblade; or Mercury Treads; because these both give Tenacity but never get both because Tenacity does NOT stack and the boots give more of it anyway.
Morello's Evil Tome; This is an item if you think you need more Cooldown Reduction which in my personal opinion Kassadin doesn't.

For early game aggression it's important to max out Null Sphere to silence and do damage. Force Pulse is also very important to slow down runners to allow for easier kills. If you are having mana problems before you finish Riley's Crystal Scepter you can get Void Blade after your ultimate instead of getting Null Void thus pushing your more offensive abilities.

For runes, I did Ability Power Per Level Glyphs, Flat Ability Power Seals, Flat Attack Speed Marks and finally two Ability Power Per Level and one Flat Attack Speed Quintessences. Runes can be changed but these are the most aggressive ones early and late game aswell.

Since this build is very offensive, I spend 29 of my points in the offensive tree and 1 in the Utility Tree. These masteries are best for earlier game but if you have a difference preference, they can be changed.

Ignite and Exhaust
The Summoner Spells can vary for this Champion, for example I prefer to take Exhaust and Ignite because these two are very good early game, in some cases before you even get your Ultimate.

Ignite changed for Teleport
The variations of this can be changing Ignite for Teleport because I understand that Ignite doesn't do as well late game with Kassadin because no one can really get away so if you prefer to sacrifice some of that early game aggression to get Teleport for overall usefulness later game. (Defending, attacking turrets or just ganking)

Exhaust or Ignite changed for Cleanse
If you are having trouble staying alive you could change either Exhaust or Ignite for Cleanse to escape those slows and stuns so you can Riftwalk away.

Exhaust or Ignite changed for Flash
Another option is to get Flash because that can be useful in defensive and offensive situations but I personally think that Riftwalk is enough.